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Pignoni, Roberto

Density and stability of Morse functions on a stratified space. (English) Zbl 0432.58003

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 6, 593-608 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0432.58003

Cited in 2 Reviews
Cited in 6 Documents

MSC:

58A35 Stratified sets
57R70 Critical points and critical submanifolds in differential topology
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory

Keywords:

density and stability of Morse functions on a stratified space

Citations:

Zbl 0307.57014
Cite Review PDF
Full Text: Numdam EuDML

References:

[1] R. Benedetti , Density of Morse functions on a complex space , Math. Ann. 229 ( 1977 ), pp. 135 - 139 . MR 457765 | Zbl 0354.32027 · Zbl 0354.32027 · doi:10.1007/BF01351598
[2] E. Brieskorn , Examples of singular normal complex spaces which are topological manifolds , Proc. Nat. Acad. Sci. U.S.A. , 55 ( 1966 ), pp. 1395 - 1397 . MR 198497 | Zbl 0144.45001 · Zbl 0144.45001 · doi:10.1073/pnas.55.6.1395
[3] F. Bruhat - H. Whitney , Quelques propriétés fondamentales des ensembles analytiques-réels , Comment. Math. Helv. , 33 ( 1959 ), pp. 132 - 160 . MR 102094 | Zbl 0100.08101 · Zbl 0100.08101 · doi:10.1007/BF02565913
[4] H. Cartan , Variétés analytiques réelles et variétés analytiques complexes , Bull, Soc. Math. France , 85 ( 1957 ), pp. 77 - 99 . Numdam | MR 94830 | Zbl 0083.30502 · Zbl 0083.30502
[5] H. Hironaka , Introduction to real-analytic sets and real-analytic maps , Istituto L. Tonelli , Pisa , 1973 . MR 477121 · Zbl 0297.32008
[6] M. Hirsch , Differential topology , Springer , 1976 . MR 448362 | Zbl 0356.57001 · Zbl 0356.57001 · doi:10.1007/978-1-4684-9449-5
[7] F. Lazzfri , Morse theory on singular spaces , Astérisque 7 et 8 , 1973 . Zbl 0307.57014 · Zbl 0307.57014
[8] S. Łojasiewicz , Ensembles semi-analytiques , Preprint I.H.E.S. , 1965 .
[9] J. Mather , Notes on topological stability , Lecture Notes , Harvard University , 1970 . · Zbl 0207.54303
[10] J. Mather , Stratifications and mappings , Proceedings of the Dynamical Systems Conference, Salvador , Brazil, July 1971 , Academic Press . MR 368064 | Zbl 0286.58003 · Zbl 0286.58003
[11] J. Milnor , Morse theory , Princeton University Press , 1963 . MR 163331 | Zbl 0108.10401 · Zbl 0108.10401
[12] R. Narasimhan , Introduction to the theory of analytic spaces , Springer , 1966 . MR 217337 | Zbl 0168.06003 · Zbl 0168.06003 · doi:10.1007/BFb0077071
[13] H. Whitney , Tangents to an analytic variety , Ann. of Math. , 81 ( 1965 ), pp. 496 - 549 MR 192520 | Zbl 0152.27701 · Zbl 0152.27701 · doi:10.2307/1970400
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